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  4. The term NOT containing x in the expansion of (1-x)2 (x+(1/x))10 is

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Q. The term NOT containing $x$ in the expansion of $\left(1-x\right)^{2} \left(x+\frac{1}{x}\right)^{10} $ is

COMEDKCOMEDK 2008Binomial Theorem

Solution:

$\left(1-x\right)^{2} \left(x+\frac{1}{x}\right)^{10} $
Term independent of x is
$^2C_0 (-x)^2 \times \,{}^{10}C_4 (x)^4 \left(\frac{1}{x} \right)^6 +\,{}^{2}C_{2}\left(-x\right)^{0 }\times\,{}^{10}C_{5} x\,{}^{5}\left(\frac{1}{x}\right)^{5}$
$ = 1\times \,{}^{10}C_{4}+1 \times ^{10}C_{5} =\,{}^{10}C_{4} +\,{}^{10}C_{5}=\,{}^{11}C_{5}$